Geometry: Identifying the Cube
A cube is a 3-D closed figure formed by 6 square faces joined along their edges. Thus all the edges of a cube are equal in length. Also, the areas of all faces of cube are also same. The cube is also called a regular hexahedron.
Parts of a cube:
Face: A cube is forms by 6 square each of which is called the face of the cube.
Edge: Each face of a cube is a square which has 4 sides each of which is called an edge.So there will be totally 12 edges in a cube.
Vertex: A point at which 3 edges meet is called the vertex of the cube. So, there will be 8 vertices in a cube.
Face diagonal: Face diagonal is a line segment joining the opposite corners of the face. Since there are 6 faces each with 2 diagonals, there are totally 6×2 = 12 face diagonals.
Space diagonals: A space diagonal is a line segment which joins the opposite corners of the cube cutting the interior. So there are 4 space diagonals in a cube.
Surface area of a cube:
The surface of the cube is contains 6 squares. So if a is the edge of each square then the area of each square is a2. So the surface area of the cube is 6 times the area of each of the square.
So, surface area of the cube = 6a2.
Volume of a cube:
The volume of a prism is nothing but the product of area of its base and its height. A cube is also a prism whose base is a square and height is same as the side length of the square.
If a is the edge of each square then the area of each square is a2. So the area of the base is a2.
So, volume of the cube = a2 x a = a3.
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